Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #92098 | C2 | semidirect |
| 2. C2×C3×C5×Q16 | C2 | semidirect |
| 3. #91831 | C2 | semidirect |
| 4. #91808 | C2 | semidirect |
| 5. #91807 | C2 | semidirect |
| 6. Q16×D15 | C2 | semidirect |
| 7. #91793 | C2 | semidirect |
| 8. #91790 | C2 | semidirect |
| 31. C2×C5×Q16 | D3 | semidirect |
| 58. C2×C3×Q16 | D5 | semidirect |
| 137. C2×Q16 | D15 | semidirect |
| 189. C3×C5 | #578 | semidirect |
| 225. C5 | #5766 | semidirect |
| 234. C3 | #66100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92098 | 2 |
| C2×C3×C5×Q16 | 2 |
| #91831 | 2 |
| #91808 | 2 |
| #91807 | 2 |
| Q16×D15 | 2 |
| #91793 | 2 |
| #91790 | 2 |
| #66100 | 3 |
| #5766 | 5 |